\subsection{一元积分比大小}
	
	\begin{ti}
		设 $I_{k} = \int_{0}^{k \uppi} \ee^{x^{2}} \sin x \dd{x} (k = 1,2,3)$，则有\kuo.

		\twoch{$I_{1} < I_{2} < I_{3}$}{$I_{3} < I_{2} < I_{1}$}{$I_{2} < I_{3} < I_{1}$}{$I_{2} < I_{1} < I_{3}$}
	\end{ti}

	\begin{ti}
		设 $N = \int_{-a}^{a} x^{2} \sin^{3}x \dd{x}$，$P = \int_{-a}^{a} \bigl( x^{3} \ee^{x^{2}} - 1 \bigr) \dd{x}$，$Q = \int_{-a}^{a} \cos^{2} x^{3} \dd{x}$，$a \geq 0$，则\kuo.

		\twoch{$N \leq P \leq Q$}{$N \leq Q \leq P$}{$Q \leq P \leq N$}{$P \leq N \leq Q$}
	\end{ti}

	\begin{ti}
		设
		\begin{align*}
			M &= \int_{-\frac{\uppi}{2}}^{\frac{\uppi}{2}} \frac{\sin x}{1 + x^{2}} \cos^{6}x \dd{x},\\
			N &= \int_{-\frac{\uppi}{2}}^{\frac{\uppi}{2}} \bigl( \sin^{3}x + \cos^{6}x \bigr) \dd{x},\\
			P &= \int_{-\frac{\uppi}{2}}^{\frac{\uppi}{2}} \bigl( x^{2} \sin^{3}x - \cos^{6}x \bigr) \dd{x},
		\end{align*}
		则\kuo.

		\twoch{$N < P < M$}{$M < P < N$}{$N < M < P$}{$P < M < N$}
	\end{ti}

	\begin{ti}
		设常数 $\alpha > 0$，积分
		\begin{align*}
			I_{1} &= \int_{0}^{\frac{\uppi}{2}} \frac{\cos x}{1 + x^{\alpha}} \dd{x},\\
			I_{2} &= \int_{0}^{\frac{\uppi}{2}} \frac{\sin x}{1 + x^{\alpha}} \dd{x},
		\end{align*}
		则\kuo.

		\onech{$I_{1} > I_{2}$}{$I_{1} < I_{2}$}{$I_{1} = I_{2}$}{$I_{1}$ 与 $I_{2}$ 的大小与 $\alpha$ 有关}
	\end{ti}

	\begin{ti}
		证明：$\int_{0}^{1} \frac{x \sin \frac{\uppi}{2} x}{1 + x} \dd{x} > \int_{0}^{1} \frac{x \cos \frac{\uppi}{2} x}{1 + x} \dd{x}$
	\end{ti}